Snap to grid using knife tool
(Edited)


Snap a 3D cursor anywhere on that X line you need.
Create a new plane.
Press R to rotate, then X to lock to X axis and rotate a plane so it would be intersecting your figure.
Go to modifiers tab and add boolen modifier.
Select your figure as an object.
Apply a modifier.


It should create a vertice on the intersection that you can use with snap tool.